In my experience hanmi is often taught with feet wide apart:.
And some teachers emphasize an a even deeper stance like shown here.

I know one teacher who likes having his feet "close together" in hanmi and just relaxes his knees instead of "going deep".
Does this so called "stance of heaven (and earth)" relate to things thought or taught concerning IS?

One way to look at it is that "heaven and earth" is not a stance, it is a method of coordinating behavior. So what position you hold your body does not matter to it, although how you coordinate your body may cause you to move in certain ways.

But wide stance, narrow stance, deep stance, high stance, is a separate issue from "heaven and earth". It refers to the idea that you can make two pathways running through the body: one channeling power down the body, another channeling power up it. Where these pathways are you can debate, but regardless, the body separates itself well at least into two actions: you've got two arms, two legs, two sides of your torso, etc. etc. and they're coordinated by two independent lobes of your brain with a tenuous amount of communication between them keeping them on the same page. The idea is to get in touch with that.

But as to the question of why you might experiment with different widths of stance is because of the overall effect they have on the angle of the legs as they run into the hips. In a higher stance, the line of the legs is more directed up, so it is perhaps more difficult for a beginner to figure out how to channel this support in horizontal directions. In a wider stance, the legs can more easily bridge force between the ground and horizontal directions, at least into the hips - getting the power up out of the hips to somewhere useful being an entirely separate and difficult bugbear.

Higher stance also means the leg/hips joints are more extended, so there is less room for them to further extend and using them to generate power will thus be trickier, but at the same time keeping the hip joint more extended will help prevent an extremely common form of structural collapse at the hip joint most people have, without them realizing it. But if you internalize the idea of extending power across the hip, rather than pushing the hip out of line, the higher stance is no longer relevant to this specifically.

But in the end, you need to learn to be comfortable channeling force with any stance to have truly free movement, by internalizing the ideas of coordination the positions may be trying to exaggerate and get you to recognize rather than just adhering to the form of things.